Their math is a bit off though... 300MW is not enough for 3.1 million households. That's 97W per household for like 2 hours.

To my understanding the use of nuclear would be to reduce the ammount of spread out battery stations that'd have to cover the base load when cloudy / at night.

There'd also be less overbuilding of solar as you have to build for winter weather and day length instead of summer if solar is supposed to cover everything

Covering winter with renewables would use longer term storage than batteries, for example hydrogen.